Reducing chaos and bifurcations in newton-type methods

  1. Amat, S. 12
  2. Busquier, S. 12
  3. Magreñán, ÁA. 12
  1. 1 Universidad Politécnica de Cartagena
    info

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Abstract and Applied Analysis

ISSN: 1085-3375

Año de publicación: 2013

Volumen: 2013

Páginas: 1-10

Tipo: Artículo

DOI: 10.1155/2013/726701 SCOPUS: 2-s2.0-84881512997 WoS: WOS:000322644700001 GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Abstract and Applied Analysis

Repositorio institucional: lock_openAcceso abierto Editor

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Resumen

We study the dynamics of some Newton-type iterative methods when they are applied of polynomials degrees two and three. The methods are free of high-order derivatives which are the main limitation of the classical high-order iterative schemes. The iterative schemes consist of several steps of damped Newton's method with the same derivative. We introduce a damping factor in order to reduce the bad zones of convergence. The conclusion is that the damped schemes become real alternative to the classical Newton-type method since both chaos and bifurcations of the original schemes are reduced. Therefore, the new schemes can be utilized to obtain good starting points for the original schemes. © 2013 S. Amat et al.